کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
420827 | 683987 | 2006 | 13 صفحه PDF | دانلود رایگان |

A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality αα. Plummer [Some covering concepts in graphs, J. Combin. Theory 8 (1970) 91–98] defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. Every well-covered graph G without isolated vertices has a perfect [1,2][1,2]-factor FGFG, i.e. a spanning subgraph such that each component is 1-regular or 2-regular. Here, we characterize all well-covered graphs G satisfying α(G)=α(FG)α(G)=α(FG) for some perfect [1,2][1,2]-factor FGFG. This class contains all well-covered graphs G without isolated vertices of order n with α⩾(n-1)/2α⩾(n-1)/2, and in particular all very well-covered graphs.
Journal: Discrete Applied Mathematics - Volume 154, Issue 9, 1 June 2006, Pages 1416–1428